New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Probability question

2007 · Shift 2 · Q8

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Advanced
Mathematics
Probability
2007 · Shift 2 · Q8

Probability question

2007 · Shift 2 · Q8

JEE AdvancedMathematicsProbabilityMCQ+3 / −1

Let

{E^c}

denote the complement of an event

E.

Let

E, F, G

be pairwise independent events with

P\left( G \right) \gt 0

and

P\left( {E \cap F \cap G} \right) = 0.

Then

P\left( {{E^c} \cap {F^c}|G} \right)

equals

A
$P\left( {{E^c}} \right) + P\left( {{F^c}} \right)$
B
$P\left( {{E^c}} \right) - P\left( {{F^c}} \right)$
C
$P\left( {{E^c}} \right) - P\left( F \right)$
D
$P\left( E \right) - P\left( {{F^c}} \right)$

More from Probability

Three students $S_{1}, S_{2},$ and $S_{3}$ are given a problem to solve. Consider the following events: U: At least one of $S_{1}, S_{2},$ and $S_{3}$ can solve the problem, V: $S_{1}$ can solve the problem, given that neither $S_{2}$ nor $S_{3}$ can solve…2025 · MCQ
A factory has a total of three manufacturing units, $M_{1}, M_{2}$ , and $M_{3}$ , which produce bulbs independent of each other. The units $M_{1}, M_{2}$ , and $M_{3}$ produce bulbs in the proportions of $2 : 2 : 1$ , respectively. It is known that $20%$ …2025 · Numerical
A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers for the remaining questions. Whenever the student knows the…2024 · MCQ
Let $X$ be a random variable, and let $P (X = x)$ denote the probability that $X$ takes the value $x$ . Suppose that the points $(x, P (X = x)), x = 0, 1, 2, 3, 4$ , lie on a fixed straight line in the $x y$ -plane, and $P (X = x) = 0$ for all $x \in R - {0, 1, 2, 3, 4}$ …2024 · Numerical
A bag contains $N$ balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume that the balls are identical otherwise. Three balls are drawn randomly one after the other without replacement. For $i = 1, 2, 3$ …2024 · Numerical
Let $X = {(x, y) \in Z \times Z : \frac{x ^{2}}{8} + \frac{y ^{2}}{20} < 1$ and $y^{2} < 5 x}$ . Three distinct points $P, Q$ and $R$ are randomly chosen from $X$ . Then the probability that $P, Q$ and $R$ …2023 · MCQ
Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the probability of a random toss resulting in head is $\frac{1}{3}$ , then the probability that the experiment stops with head is :2023 · MCQ
Let $X$ be the set of all five digit numbers formed using 1,2,2,2,4,4,0. For example, 22240 is in $X$ while 02244 and 44422 are not in $X$ . Suppose that each element of $X$ has an equal chance of being chosen. Let $p$ be the conditional…2023 · Numerical